Mtgirl, my recommendation would be to look for a vintage machine that was kept in good condition. In my opinion, you'll enjoy sewing so much more if you have a decent machine; if you own a cheap machine, it will sit in the closet and will only be pulled out if you have to hem something. There are lots of excellent vintage machines out there. Try posting a notice in a seniors' residence or a fabric store, check with a local sewing machine dealer, visit a garage/tag sale in an older neighborhood, or even just ask friends' mothers and grandmothers. I'll bet you'll find a something for less than $50. Add another $50-$75 for a tune-up and you'll have a machine that will sew circles around anything that you can pick up in Target or Walmart, or Sears.
Look for a high-end, European machine--Viking/Husqvarna, Bernina, or Pfaff are all good makes. Look for a 25-35 year old machine with a metal chassis and mechanical components, with limited or no electronic parts. If the machine has been well-looked after, it will come with all the original accessories and probably even the original manual and case. The machine should still be in very good condition if it's been used with love and care, and stored properly.
You'll want a free arm that's narrow enough to work on all kinds of narrow diameter sewing and an easy buttonhole feature. All of these machine will have a variety of zigzag stitches and adjustable needle positions; check to make sure that the knobs still move freely. Some machines will have automatic needle threaders, levers instead of screws to remove and replace needles and feet, automatic tension adjustment, and other special features. You should also get a handful of different feet so you can blind-hem, sew on buttons, insert zippers, and perform a host of other operations.
My DIL is now using my 35 year-old Bernina instead of her cheap Kenmore and can't believe how much easier it is to sew on the vintage machine. I'm currently using a 30 year-old Pfaff that belonged to my mother which is still a beautiful machine. A precision sewing machine can be cheap as chips these days if you just take a bit of time to locate one whose owner is willing to pass it on to the next generation. And you might get the odd sewing lesson thrown in for free as well!